Linear Elastic Analysis

Perform a linear elastic analysis for comparison purposes.

Abaqus includes a three-dimensional continuum element (e.g., C3D8R) that can utilize a multilayer composite lay-up. The use of continuum elements that explicitly account for all six stress components (σ₁₁, σ_22, σ₃₃, σ₁₂, σ_13, σ₂₃) ensures that the material failure criteria can utilize the transverse stress components (σ₃₃, σ_13, σ₂₃) that are neglected (or only approximated) in conventional or continuum shell elements. To demonstrate the importance of explicitly accounting for the transverse stress components, a simple linear elastic analysis is performed to allow comparison of the magnitudes of the in-plane and transverse stress components in the most highly stressed region of the model.

Model

ASCA_EP1_linear_elastic_solid.inp

• Element type: C3D8R
• Through-thickness mesh density:
  • Composite Facesheets: 1 element
  • Foam Core: 1 element

Results

The image below displays the stress state for a point in the outside surface ply near the upper left-hand corner of the access door of the composite conic. The fiber constituent failure criterion is dependent on three stress components (σ₁₁, σ₁₂, σ₁₃). Further examination reveals that the transverse shear stress (σ₁₃) is negligible in comparison to the in-plane stresses (e.g., σ₁₃ is only 0.1% of σ₁₁). This indicates that transverse stresses will not provide a significant contribution to fiber failure. On the other hand, matrix constituent failure is driven by all six stress components. By comparing the magnitude of the out-of-plane stresses (σ₃₃, σ_13, σ₂₃) with the magnitude of the in-plane stresses (σ₂₂, σ₁₂), we can see that the out-of-plane stresses will make a significant contribution to the matrix failure criterion. To accurately predict failure in the structure, matrix failure must be captured properly, because after a matrix failure event, the matrix constituent stiffness is reduced and stress redistribution causes an increase in stress in the fibers.

Because the transverse stresses are not negligible in certain regions of large composite structures, it is recommended that solid elements be used wherever possible. This will be demonstrated later when solid elements are compared with continuum shell elements (Effect of Element Type on Progressive Failure Response).